Reduced state sequence estimation with soft decision outputs

ABSTRACT

A receiver may be operable to receive an inter-symbol correlated (ISC) signal, and generate a plurality of soft decisions as to information carried in the ISC signal. The soft decisions may be generated using a reduced-state sequence estimation (RSSE) process. The RSSE process may be such that the number of symbol survivors retained after each iteration of the RSSE process is less than the maximum likelihood state space. The plurality of soft decisions may comprise a plurality of log likelihood ratios (LLRs). Each of the plurality of LLRs may correspond to a respective one of a plurality of subwords of a forward error correction (FEC) codeword.

CROSS-REFERENCE TO RELATED APPLICATIONS/INCORPORATION BY REFERENCE

This patent application is a continuation of U.S. patent applicationSer. No. 14/187,436 filed Feb. 24, 2014, now U.S. Pat. No. 8,948,321,which is a continuation of U.S. patent application Ser. No. 13/922,329filed Jun. 20, 2013, now U.S. Pat. No. 8,666,000, which makes referenceto, claims priority to, and claims benefit from:

U.S. Provisional Patent Application Ser. No. 61/662,085 entitled“Apparatus and Method for Efficient Utilization of Bandwidth” and filedon Jun. 20, 2012, now expired;

U.S. Provisional Patent Application Ser. No. 61/726,099 entitled“Modulation Scheme Based on Partial Response” and filed on Nov. 14,2012, now expired;

U.S. Provisional Patent Application Ser. No. 61/729,774 entitled“Modulation Scheme Based on Partial Response” and filed on Nov. 26,2012, now expired;

U.S. Provisional Patent Application Ser. No. 61/747,132 entitled“Modulation Scheme Based on Partial Response” and filed on Dec. 28,2012, now expired;

U.S. Provisional Patent Application Ser. No. 61/768,532 entitled “HighSpectral Efficiency over Non-Linear, AWGN Channels” and filed on Feb.24, 2013, now expired; and

U.S. Provisional Patent Application Ser. No. 61/807,813 entitled “HighSpectral Efficiency over Non-Linear, AWGN Channels” and filed on Apr. 3,2013, now expired.

Each of the above applications is hereby incorporated herein byreference in its entirety.

This application also makes reference to:

U.S. Pat. No. 8,582,637, titled “Low-Complexity,Highly-Spectrally-Efficient Communications”;

U.S. Pat. No. 8,897,387, titled “Design and Optimization of PartialResponse Pulse Shape Filter”;

U.S. Pat. No. 8,675,769, titled “Constellation Map Optimization forHighly Spectrally Efficient Communications”;

U.S. Pat. No. 8,571,131, titled “Dynamic Filter Adjustment forHighly-Spectrally-Efficient Communications”;

U.S. Pat. No. 8,559,494, titled “Timing Synchronization for Reception ofHighly-Spectrally-Efficient Communications”;

U.S. Pat. No. 8,559,496, titled “Signal Reception UsingNon-Linearity-Compensated, Partial Response Feedback”;

U.S. Pat. No. 8,599,914, titled “Feed Forward Equalization forHighly-Spectrally-Efficient Communications”;

U.S. Pat. No. 8,665,941, titled “Decision Feedback Equalizer for HighlySpectrally Efficient Communications”;

U.S. Pat. No. 8,873,612, titled “Decision Feedback Equalizer withMultiple Cores for Highly-Spectrally-Efficient Communications”;

U.S. Pat. No. 8,559,498, titled “Decision Feedback Equalizer UtilizingSymbol Error Rate Biased Adaptation Function for Highly SpectrallyEfficient Communications”;

U.S. Pat. No. 8,548,097, titled “Coarse Phase Estimation ForHighly-Spectrally-Efficient Communications”;

U.S. Pat. No. 8,565,363, titled “Fine Phase Estimation for HighlySpectrally Efficient Communications”;

U.S. Pat. No. 8,744,003, titled “Multi-Mode Transmitter forHighly-Spectrally-Efficient Communications”;

U.S. Pat. No. 8,605,832, titled “Joint Sequence Estimation of Symbol andPhase With High Tolerance Of Nonlinearity”;

U.S. Pat. No. 8,553,821, titled “Adaptive Non-Linear Model forHighly-Spectrally-Efficient Communications”;

U.S. Pat. No. 8,824,599, titled “Pilot Symbol-Aided Sequence Estimationfor Highly-Spectrally-Efficient Communications”;

U.S. Pat. No. 8,571,146, titled “Method and System for Corrupt SymbolHandling for Providing High Reliability Sequences”;

U.S. Pat. No. 8,566,687, titled “Method and System for Forward ErrorCorrection Decoding with Parity Check for Use in Low ComplexityHighly-spectrally-efficient Communications”;

U.S. patent application Ser. No. 13/755,061 , titled “Method and Systemfor Quality of Service (QoS) Awareness in a Single Channel CommunicationSystem,” and filed on Jan. 31, 2013;

U.S. Pat. No. 8,665,992, titled “Pilot Symbol Generation forHighly-Spectrally-Efficient Communications”;

U.S. Pat. No. 8,548,072, titled “Timing Pilot Generation forHighly-Spectrally-Efficient Communications”;

U.S. Pat. No. 8,842,778, titled “Multi-Mode Receiver forHighly-Spectrally-Efficient Communications”;

U.S. Pat. No. 8,572,458, titled “Forward Error Correction with ParityCheck Encoding for use in Low Complexity Highly-spectrally-efficientCommunications”; and

U.S. Pat. No. 8,526,523, titled “Highly-Spectrally-Efficient Receiver”.

Each of the above applications is hereby incorporated herein byreference in its entirety.

FIELD

Certain embodiments of the disclosure relate to communication systems.More specifically, certain embodiments of the disclosure relate to amethod and system for improving bit error rate (BER) performance basedon a sequence estimation algorithm and forward error correction (FEC).

BACKGROUND

Existing communications methods and systems are overly power hungryand/or spectrally inefficient. Complex linear modulation schemes suchas, for example, quadrature amplitude modulation (QAM), are used vastlyin wireless and non-wireless communications. However, performance ofsuch modulation schemes degrades in the presence of phase noise andnon-linear distortion associated with the communication channel. Some ofthese modulation schemes may perform, for example, 4-5 dB below theShannon capacity bound in the case of severe phase noise. Ashigher-order modulation is needed to drive more throughput, the resultmay be a throughput that is even further away from the Shannon capacitylimit. That is, the gap between maximum spectral efficiency and actualspectral efficiency may actually increase with increasing QAM order. Inaddition, higher-order modulation may also be increasingly sensitive tonon-linear distortion.

Further limitations and disadvantages of conventional and traditionalapproaches will become apparent to one of skill in the art, throughcomparison of such systems with the present disclosure as set forth inthe remainder of the present application with reference to the drawings.

BRIEF SUMMARY OF THE DISCLOSURE

Aspects of the present disclosure are directed to a method and systemfor improving bit error rate (BER) performance based on a sequenceestimation algorithm and forward error correction (FEC), substantiallyas shown in and/or described in connection with at least one of thefigures, as set forth more completely in the claims.

Various advantages, aspects and novel features of the presentdisclosure, as well as details of an illustrated embodiment thereof,will be more fully understood from the following description anddrawings.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram illustrating an example communication system,in accordance with an embodiment of the disclosure.

FIG. 2A is a block diagram illustrating an example coupling of anequalizer and a sequence estimation module in a receiver, in accordancewith an embodiment of the disclosure.

FIG. 2B is a block diagram illustrating an example sequence estimationmodule in a receiver, in accordance with an embodiment of thedisclosure.

FIG. 3 is a diagram illustrating example symbol survivors, in accordancewith an embodiment of the disclosure.

FIGS. 4A-4F illustrate generation of example histograms from symbolsurvivors in a RSSE circuit, in accordance with an embodiment of thedisclosure.

DETAILED DESCRIPTION

As utilized herein, “and/or” means any one or more of the items in thelist joined by “and/or”. As an example, “x and/or y” means any elementof the three-element set {(x), (y), (x, y)}. As another example, “x, y,and/or z” means any element of the seven-element set {(x), (y), (z), (x,y), (x, z), (y, z), (x, y, z)}. As utilized herein, the term “exemplary”means serving as a non-limiting example, instance, or illustration. Asutilized herein, the terms “e.g.,” and “for example” set off lists ofone or more non-limiting examples, instances, or illustrations. Asutilized herein, a device/module/circuitry/etc. is “operable” to performa function whenever the device/module/circuitry/etc. comprises thenecessary hardware and code (if any is necessary) to perform thefunction, regardless of whether performance of the function is disabled,or not enabled, by some user-configurable setting.

FIG. 1 is a block diagram illustrating an example communication system,in accordance with an embodiment of the disclosure. Referring to FIG. 1,there is shown a communication system 100. The communication system 100may comprise a transmitter 120, a communication channel 108 and areceiver 130. The transmitter 120 may comprise, for example, a FECencoder 101 and a word-to-symbol module 102. The receiver 130 maycomprise, for example, a sequence estimation module 112, asymbol-to-word module 114 and a FEC decoder 116. A total partialresponse filtering function may be split between the transmitter 120 andthe receiver 130. In this regard, the transmitter 120 may comprise apulse shaper 104 and the receiver 130 may comprise an input filter 105.The total partial response filtering function may be split between thepulse shaper 104 and the input filter 105. In an example embodiment ofthe disclosure, other components such as, for example, an interleaver inthe transmitter 120, a timing recovery module in the receiver 130,and/or a de-interleaver in the receiver 130 may also be optionallyincluded without departing from the spirit and scope of variousembodiments of the disclosure.

The FEC encoder 101 may comprise suitable logic, circuitry, interfacesand/or code that may be operable to generate codewords from the inputdata bitstream. Each codeword may comprise one or more informationsubwords and one or more parity subwords to enable error correction inthe receiver 130. Each subword may be a bit or may be a symbol. The FECcodewords may be generated, for example, in accordance with aReed-Solomon (RS) code. Forward error correction (FEC) may be used tofix communication errors caused by a communication channel such as thechannel 108. Using a good and suitable FEC may improve spectralefficiency of the system 100 and enable it to perform close to theShannon capacity bound. However, using FEC may introduce overhead, theamount of which depends on the FEC code rate.

The mapper module 102 may comprise suitable logic, circuitry, interfacesand/or code that may be operable to map codewords to symbols accordingto, for example, a linear modulation scheme such as a quadratureamplitude modulation (QAM). In this regard, an M-QAM may comprise atotal of M symbols in a QAM symbol constellation over an I-Q plane (M isa positive integer). For example, a 32-QAM symbol constellation maycomprise a total of 32 symbols. A modulation symbol constellation 150 isalso illustrated in FIG. 1. In an example implementation, each FECcodeword output by encoder 101 may comprise S subwords, each subword maycomprise L bits, and every log₂(M)/L of the S subwords may be mapped toa constellation symbol by module 102.

Although M-QAM is used for illustration in this disclosure, aspects ofthis disclosure are applicable to any modulation scheme (e.g., amplitudeshift keying (ASK), phase shift keying (PSK), frequency shift keying(FSK), etc.). Additionally, points of the M-QAM constellation may beregularly spaced (“on-grid”) or irregularly spaced (“off-grid”).

The pulse shaper 104 may comprise suitable logic, circuitry, interfacesand/or code that may be operable to adjust the waveform of a signalreceived from the mapper module 102 such that the waveform of aresulting signal complies with the spectral requirements of acommunication channel such as the channel 108. The spectral requirementsmay be referred to as the “spectral mask” and may be established by aregulatory body (e.g., the Federal Communications Commission in theUnited States or the European Telecommunications Standards Institute)and/or a standard body (e.g., Third Generation Partnership Project) thatgoverns the communication channels and/or standards in use.

The input filter 105 may comprise suitable logic, circuitry, interfacesand/or code that may be operable to adjust the waveform of the signalreceived via the channel 108 to generate a signal for further processingin the receiver 130.

Each of the pulse shaper 104 and the input filter 105 may comprise, forexample, an infinite impulse response (IIR) and/or a finite impulseresponse (FIR) filter. The number of taps in the pulse shaper 104 isdesignated LTx and the number of taps in the input filter 105 isdesignated LRx. The impulse response of the pulse shaper 104 is denotedherein as hTx and the impulse response of the input filter 105 isdenoted herein as hTRx.

In an example embodiment of the disclosure, in order to improvetolerance of non-linearity, the pulse shaper 104 and the input filter105 may be configured such that each of the output signal of the pulseshaper 104 and the output signal of the input filter 105 intentionallyhas a substantial amount of inter-symbol interference (ISI). In thisregard, the ISI is therefore a controlled ISI. Accordingly, the pulseshaper 104 may be referred to as a partial response pulse shapingfilter, and the resulting (output) signals of the pulse shaper 104 andthe input filter 105 may be referred to as partial response signals oras residing in the partial response domain. The number of the tapsand/or the values of the tap coefficients of the input filter 105 may bedesigned such that it is intentionally non-optimal in terms of noise inorder to improve the tolerance of non-linearity. In this regard, thepulse shaper 104 and/or the input filter 105 in the system 100 may offersuperior performance in the presence of non-linearity as compared to,for example, a conventional near zero positive ISI pulse shaping filtersuch as a raised cosine (RC) pulse shaping filter or a pair ofroot-raised cosine (RRC) pulse shaping filters.

It should be noted that a partial response signal (or signals in the“partial response domain”) is just one example of a type of signal forwhich there is correlation among symbols of the signal (referred toherein as “inter-symbol-correlated (ISC) signals”). Such ISC signals arein contrast to zero (or near-zero) ISI signals generated by, forexample, raised-cosine (RC). For simplicity of illustration, thisdisclosure focuses on partial response signals generated via partialresponse filtering. Nevertheless, aspects of this disclosure areapplicable to other ISC signals such as, for example, signals generatedvia matrix multiplication (e.g., lattice coding), and signals generatedvia decimation as in multi carrier applications such as in OFDM systems.

A “total partial response (h)” may be equal to the convolution of hTxand hRx, and, thus, the “total partial response length (L)” may be equalto LTx+LRx−1. L may, however, be chosen to be less than LTx+LRx−1 where,for example, one or more taps of the pulse shaper 104 and/or the inputfilter 105 are below a determined level. Reducing L may reduce decodingcomplexity of a sequence estimation process in the receiver 130. Thistradeoff may be optimized during the design of the pulse shaper 104 andthe input filter 105 in the system 100.

The Tx media matching module 107 may comprise suitable logic, circuitry,interfaces and/or code that may be operable to transform the partialresponse signal outputted by the pulse shaper 104 to an appropriatesignal needed to drive the media in the channel 108. For example, the Txmedia matching module 107 may comprise a power amplifier, a radiofrequency (RF) up-converter, an optical transceiver for opticalapplication, and/or other transformation device which may be requiredfor propagating over the media.

The Rx media matching module 109 may comprise suitable logic, circuitry,interfaces and/or code that may be operable to convert the signal comingfrom the media in the channel 108 to baseband signal for processing ordemodulating. For example, the Rx media matching module 109 may comprisea power amplifier, a radio frequency (RF) down-converter, an opticaltransceiver for optical application, and/or other transformation device.

The channel 108 may comprise suitable logic, circuitry, device,interfaces and/or code that may be operable to transmit signals from thetransmitter 120 to the receiver 130. The channel 108 may comprise awired, wireless and/or optical communication medium. The channel 108 maycomprise noise such as, for example, additive white Gaussian noise(AWGN). The channel 108 may also introduce distortions such as multipathand fading. In an example embodiment of the disclosure, signalstransmitted over the channel 108 may include distortion such as, forexample, phase noise and/or non-linear distortion. In this regard, forexample, the channel 108 may receive signals from the transmitter 120via a Tx media matching module 107 which transforms the partial responsesignal outputted by the pulse shaper 104 to an appropriate signal neededto drive the media in the channel 108. The receiver 130 may receivesignals from the channel 108 via an Rx media matching module 109 whichconverts the signal coming from the media to baseband for demodulating.Both the Tx media matching module 107 and the Rx media matching module109 may introduce distortion such as phase noise and non-lineardistortion (and/or other non-idealities) caused by, for example, limiteddynamic range of components. For example, in radio applications,frequency sources may be needed for up-converting the partial responsesignal outputted by the pulse shaper 104 from baseband to radiofrequency (RF). The frequency sources may introduce phase noise whichmay distort the phase of the modulated signal. Non-linear distortion(e.g., 3^(rd) order) may be generated by elements such as, for example,mixers, power amplifiers, variable attenuators and/or baseband analogamplifiers.

The equalizer 110 may comprise suitable logic, circuitry, interfacesand/or code that may be operable to perform equalization functions forthe receiver 130. The equalizer 110 may be operable to process a signalreceived by the equalizer 110 to reduce, for example, ISI caused by thechannel 108 between the transmitter 120 and the receiver 130. In anexample embodiment of this disclosure, the input signal of the equalizer110 may be a partial response signal received via the channel 108. Inthis regard, the output signal of the equalizer 110 may be a partialresponse signal where the ISI left in the output signal may be primarilythe result of the pulse shaper 104 and/or the input filter 105 (theremay be some residual ISI from multipath, for example, due to use of aleast-mean-square (LMS) approach in the equalizer 110). In an exampleembodiment of the disclosure, the equalizer 110 may be adapted based onan error signal that may be generated in reference to a reconstructedsignal (e.g., a reconstructed partial response signal) generated by thesequence estimation module 112.

The sequence estimation module 112 may comprise suitable logic,circuitry, interfaces and/or code that may be operable to performsequence estimation functions for the receiver 130. The sequenceestimation module 112 may be operable to output soft-decisions,hard-decisions, or both. The soft-decisions may be calculated aslog-likelihood ratios (LLRs). For a binary code, this ratio is definedas the log of the ratio of the (a posteriori) probabilities that atransmitted bit, d_(k), was a “1” or “0”, respectively (or vice versa),based on the received version of that bit, y_(k).

$\begin{matrix}{{\Lambda\left( d_{k} \right)} = {\log{\frac{P\left( {d_{k} = {{``1"}❘y_{k}}} \right)}{P\left( {d_{k} = {{``0"}❘y_{k}}} \right)}.}}} & (1)\end{matrix}$For an M-ary code, each code symbol may be assigned (M−1) soft valuesdefined as the log of the ratio of the probability of that symbol beingone of the values of the alphabet et and the probability that thissymbol was transmitted as the arbitrarily chosen predefined symbolreference denoted by S₀:

$\begin{matrix}{{{\Lambda\left( {d_{k} = S_{j}} \right)} = {\log\frac{P\left( {d_{k} = {S_{j}❘y_{k}}} \right)}{P\left( {d_{k} = {S_{0}❘y_{k}}} \right)}}},{j = 1},2,\ldots\mspace{14mu},{M - 1.}} & (2)\end{matrix}$

Iterative decoding techniques employ soft-decision decoding algorithmsthat also provide soft-decision output. The traditional Viterbialgorithm is a soft-decision decoding algorithm that does not calculatesoft-decision output. A modified version of this algorithm, theso-called Soft-Output Viterbi Algorithm (SOVA) produces that softoutput. This algorithm maintains a symbol survivor per each code(trellis) state (similarly to the traditional Viterbi algorithm) inaddition to an LLR (soft decision) per each bit (in some range withrespect to the present symbol time) and code state. This soft decisionquantifies the reliability of that bit, provided that the final decisionis in favor of the respective code state. This soft decision may bedefined as the log of the probability of the best trellis path that endsin the code state under discussion and the probability of a second paththat terminates in this state. This second path is the best path thatterminates in this same state in which the bit under discussion takes onthe opposite value relative to its value on the best path that ends inthe state under discussion. In general, at each symbol time (trellisbranch) or once per a few symbol times, the soft-decision decodingalgorithm decides on the best trellis state and traces back themaintained information to a given decision delay and it routes out thesoft-values associated with the winner trellis state at that trace-backdepth. Clearly, tracing back the surviving paths, they tend to coincideinto the same history path for a sufficiently large decoding delay(relative to the most recent symbol). Thus, when the soft-values (oralso hard decisions) are read off with some sufficient delay, they areassumed to be reliable.

In implementations in which the sequence estimation module 112 maintainsfull state information (e.g., the information required for optimummaximum-likelihood sequence estimation), an algorithm such as SOVA maybe used for generating soft symbol estimates. In practice, however, thecomplexity of such an implementation would rapidly become unwieldy asthe size of the symbol constellation increases.

In implementations in which the sequence estimation module 112 uses areduced-state sequence estimation algorithm, full state information isnot available and, consequently, algorithms such as SOVA areinapplicable. Accordingly, in such implementations, information aboutsymbol survivors may be used to generate soft decisions. In oneimplementation, soft decisions may be generated per-subword of an FECcodeword. In one such implementation, the soft decisions (e.g.,formatted as LLRs) may not be associated with individual survivor pathsor states. Instead, a single soft-decision for a subword may begenerated based on a plurality of survivors. For example, thesoft-values may be derived from a symbol histogram generated for therespective trellis branch. Per a transmitted constellation symbol ortrellis branch, a symbol histogram is generated and retained overmultiple iterations of the sequence estimation process. This histogramrelates some measure, or probability, for interpreting the receivedsymbol, at that symbol time, as one of the possible constellationsymbols or FEC symbols. Thus the length of this histogram may be M,where M is the size of the symbol constellation used for modulation.Example histograms are described below with reference to FIGS. 4A and4B.

The FEC decoder 116 may comprise suitable logic, circuitry, interfacesand/or code that may be operable to utilize the parity subwords of theFEC codewords to correct errors. For example, the FEC decoder 116 may bea Reed-Solomon (RS) decoder, Low Density Parity Check (LDPC) code, a socalled Turbo Code scheme (such as a Parallel Concatenated Code—PCC), ora concatenated coding scheme that includes an inner code scheme inaddition to another outer code.

FIG. 2A is a block diagram illustrating an example coupling of anequalizer and a sequence estimation module in a receiver, in accordancewith an embodiment of the disclosure. Referring to FIG. 2A, there isshown the equalizer 110 and the sequence estimation module 112. Thesequence estimation module 112 may incorporate a non-linear model 210 ina sequence estimation process. The equalizer 110 and the sequenceestimation module 112 may be as described with respect to FIG. 1, forexample.

In the exemplary embodiment of the disclosure illustrated in FIG. 2A,although the equalizer 110 and the sequence estimation module 112 areshown, the disclosure may not be so limited. Other modules (or circuits)such as, for example, a carrier recovery module, a phase adjust moduleand/or other similar modules may also be optionally included in FIG. 2Awithout departing from the spirit and scope of various embodiments ofthe disclosure. For example, the carrier recovery module and/or thephase adjust module may be included for various phase correction orrecovery throughout the equalization process and/or the sequenceestimation process.

The non-linear model 210 may comprise, for example, a saturated thirdorder polynomial which may be expressed as

$\begin{matrix}{y = \left\{ {{\begin{matrix}{{x \cdot \left( {1 - {r \cdot {\mathbb{e}}^{j\;\varphi} \cdot {x}^{2}}} \right)},} & {x < x_{sat}} \\{y_{sat},} & {x \geq x_{sat}}\end{matrix}y_{sat}} = {x_{sat} \cdot \left( {1 - {r \cdot {\mathbb{e}}^{j\;\varphi} \cdot {x_{sat}}^{2}}} \right)}} \right.} & \lbrack 1\rbrack\end{matrix}$where, x_(sat) denotes the input saturation value, y_(sat) denotes theoutput saturation value, x denotes an input of a non-linear device (orgroup of devices), y denotes an output of the non-linear device (orgroup of devices), and γ may be set according to a desired distortionlevel (backoff). For example, the non-linear device may be a poweramplifier in the Tx media matching module 107. In this regard, the x inequation [1] may denote an input power level of the power amplifier andthe y may denote an output power level of the power amplifier. Increasedaccuracy resulting from the use of a higher-order polynomial for thenon-linear model 210 may tradeoff with increased complexity ofimplementing a higher-order polynomial. As transmitter's non-linearitymay be the dominant non-linearity of the communication system 100,modeling the transmitter's non-linearity may be sufficient. In instanceswhere degradation in a receiver's performance is above a certainthreshold due to other non-linearities in the system (e.g.,non-linearity of the Rx media matching module 109), the non-linear model210 may take into account such other non-linearities. Equation 1represents just one example of a non-linearity model that may be used bythe module 112 in one or more embodiments of the disclosure.

In an example operation, the equalizer 110 may be operable to process orequalize a signal 201 to reduce, for example, ISI caused by the channel108. The equalizer adaptation may be based on, for example, a LMSalgorithm. An error signal 205 is fed back to the equalizer 110 to drivethe adaptive equalizer 110. The reference for generating the errorsignal 205 may be, for example, a reconstructed signal 203 coming fromthe sequence estimation module 112. In an example embodiment of thedisclosure, the signal 201 may be a partial response signal. In thisregard, the reconstructed signal 203 may be a reconstructed partialresponse signal. The error signal 205 is the difference, calculated by acombiner 204, between an output signal 202 of the equalizer 110 and thereconstructed signal 203. Generation of the reconstructed signal 203 mayincorporate the non-linear model 210 of the signal 201 and is describedbelow with reference to FIG. 2B. An equalized signal 230 may be inputtedto the sequence estimation module 112. The sequence estimation module112 may be operable to generate symbols (estimated symbols) 240, fromthe signal 230, using the sequence estimation process. The generatedsymbols 240 may be hard and/or soft estimates of transmitted symbolsgenerated by the mapper module 102 in the transmitter 120. An exampleimplementation of the sequence estimation module 112 is described belowwith reference to FIG. 2B.

FIG. 2B is a block diagram illustrating an example sequence estimationmodule in a receiver, in accordance with an embodiment of thedisclosure. Referring to FIG. 2B, there is shown the sequence estimationmodule 112. The sequence estimation module 112 may comprise, forexample, a symbol candidate generation module 202, a metrics calculationmodule 204, a symbol survivor selection module 206, a symbol estimationmodule 220 and a signal reconstruction module 224. The sequenceestimation process described with respect to FIG. 2B is an example only.Many variations of the sequence estimation process may also be possible.The sequence estimation module 112 may be as described with respect toFIGS. 1 and 2A, for example.

The metrics calculation module 204 may comprise suitable logic,circuitry, interfaces and/or code that may be operable to generatemetrics needed for symbol survivor selections and symbol (includingcorresponding phase) estimations. Metrics calculations may be executedbased on a signal 230 received by the metrics calculation module 204 andsymbol candidates generated by the symbol generation module 202. Eachsymbol candidate may be a vector comprising, for example, Q candidatesymbols (Q is a positive integer). Information associated with the tapsof the pulse shaper 104 and/or the input filter 105 may also be utilizedfor the metrics calculation. In an example embodiment of the disclosure,the signal 230 may be a partial response signal received from the inputfilter 105. The taps information (e.g., number of taps and/or tapcoefficients) associated with the pulse shaper 104 and/or the inputfilter 105 may be used to generate reconstructed partial response signalcandidates from the symbol candidates, for example, via convolution. Thetaps information associated with the pulse shaper 104 and/or the inputfilter 105 may be presented, for example, in the form of (LTx+LRx−1) tapcoefficients corresponding to the total partial response h, according tothe LTx tap coefficients of the pulse shaper 104 and the LRx tapcoefficients of the input filter 105. Furthermore the non-linear model210 may be incorporated in the process of generating the reconstructedpartial response signal candidates. For example, the non-linear model210 may be applied to the convolved symbol candidates to generate thereconstructed partial response signal candidates. The metric value foreach of the symbol candidates may then be generated based on a costfunction (e.g., a squared error function) between the signal 230 and thereconstructed partial response signal candidates. One or more candidateswhich have the best metrics level may be selected by the symbol survivorselection module 206 for the next iteration of the sequence estimationprocess.

The symbol survivor selection module 206 may comprise suitable logic,circuitry, interfaces and/or code that may be operable to performmetrics sorting and selection of a determined number of symbol survivorsbased on the metrics associated with the symbol candidates. In thisregard, for example, one or more candidates which have the lowestmetrics level may be selected, from among the symbol candidates, assymbol survivors. Where the module 112 implements a reduced statesequence estimation (RSSE) algorithm, the number of survivors selectedby the module 206 for the next iteration may be smaller than the size ofthe corresponding Maximum Likelihood state space. For example, for M-QAMand total partial response length L, the number of survivors selectedfor the next iteration may be less than M^(L−1). Each symbol survivormay also be a vector comprising, for example, Q candidate symbols (Q isa positive integer). Each element of each symbol survivor may comprise asoft-decision estimate and/or a hard-decision estimate of a symbol ofthe signal 230. Besides a newly-detected symbol at a head of the vector,there are (Q−1) symbols in the vector. Some of the (Q−1) symbols couldbe different than corresponding symbols in a previously-selected symbolsurvivor (i.e. the sequence estimation may diverge to a differentvector). The reliability of the newly-detected symbol may be very lowbecause it may be derived only from the newest signal sample and a firsttap of the (LTx+LRx−1) taps associated with the pulse shaper 104 and/orthe input filter 105, which may have a coefficient that is small inmagnitude. The reliability of old symbols toward a tail of the vectormay improve along the survived vectors because old symbols arerepresented by many signal samples (up to effective number of the tapsof the total partial response) and thus take advantage of moreinformation. In this regard, the tails (old symbols) of the symbolsurvivors may converge to the same solution while the head (youngsymbols) parts of the symbol survivors may be different.

The symbol candidate generation module 202 may comprise suitable logic,circuitry, interfaces and/or code that may be operable to generatesymbol candidates from symbol survivors generated from a previousiteration of the sequence estimation process. For example, for M-OAM (Mis a positive integer), there are M symbols in the M-QAM symbolconstellation (e.g., the modulation symbol constellation 150) over anI-Q plane. In this regard, generation of the symbol candidates maycomprise, for example, duplicating (e.g., (M−1) times) each of thesymbol survivors (vectors) generated during the previous iteration ofthe sequence estimation process, shifting each of the resulting Mvectors by one symbol position toward the tail of the vector, and thenfilling each of the M vacant symbol positions (at the head of thevector) with a symbol from among the M possible symbols in the M-QAMsymbol constellation (e.g., the modulation symbol constellation 150).

The symbol estimation module 220 may comprise suitable logic, circuitry,interfaces and/or code that may be operable to generate hard and/or softdecisions based on the symbol survivors received from the symbolsurvivor selection module 206. The symbol estimation module 220 maycomprise one or more buffers to store one or more symbol survivors. Inan example implementation, a hard decision output by module 220 may be asymbol determined to be the most-likely transmitted symbol correspondingto a sample of signal 230. In an example implementation, a hard decisionoutput by module 220 may be a subword determined to be the most-likelytransmitted subword corresponding to a sample of signal 230. In anexample implementation, a soft decision output by module 220 maycomprise a plurality of LLRs indicating, for a sample of the signal 230,the respective probabilities of each of a plurality of possible subwordvalues of a FEC codeword.

Operation of an example symbol estimation module 220 is described belowwith reference to FIG. 3.

The signal reconstruction module 224 may comprise suitable logic,circuitry, interfaces and/or code that may be operable to generate thereconstructed signal 203. In an example embodiment of the disclosure,the signal 230 may be an equalized partial response signal received fromthe equalizer 110. The taps information associated with the pulse shaper104 and/or the input filter 105 (e.g., the (LTx+LRx−1) tap coefficients)may be used to generate the reconstructed signal (partial responsesignal) 203 from the estimated symbols 240, for example, viaconvolution. In this regard, for example, the non-linear model 210 maybe incorporated in the process of generating the reconstructed signal(partial response signal) 203. For example, the non-linear model 210 maybe applied to the convolved symbols to generate the reconstructed signal(partial response signal) 203.

FIG. 3 is a diagram illustrating example symbol survivors, in accordancewith an embodiment of the disclosure. Referring to FIG. 3, there isshown a best symbol survivor 300 and a plurality of other symbolsurvivors, of which symbol survivors 301-303 are illustrated. Each ofthe symbol survivors 300-303 may comprise a vector of estimated symbolvalues, the values selected from among the values of a symbolconstellation (such as the modulation symbol constellation 150) used ingenerating the signal being decoded. The length of the vector may bedetermined or designed, for example, based on the total partial responselength L (e.g., L=LTx+RTx−1). For example, the length of the vector maybe five times the length of the total partial response length L. ForM-QAM (M is a positive integer), there are a total of M possible symbolvalues in the M-QAM constellation over an I-Q plane. For example, for a32-QAM, there are a total of 32 symbol values in the 32-QAM symbolconstellation.

There is also shown in FIG. 3, a converged region 310 toward a tail ofthe vector, a diverged region 320 toward a head of the vector and anobservation region 312 which is within the diverged region 320 yetadjacent to the converged region 310. For each iteration of the sequenceestimation process performed by the sequence estimation module 112, aleft-most element of each of the symbol survivors 300-303 holds anestimated symbol value for symbol time n, a second element holds anestimated symbol value for symbol time n−1, and so on. Thus, as timeprogresses, estimated symbol values for particular points in time willshift to the right in the symbol survivors. In other words, “older”estimated symbol values (i.e., value with longer decision delay) are tothe right in FIG. 3 and “newer” estimated symbol values (i.e., valueswith shorter decision delay) are to the left in FIG. 3. Because olderestimated symbol values are based on more information (e.g., based onmore filter taps) the older estimated symbol values will tend to be thesame across the various symbol survivors 300-303 (i.e., the estimatedsymbol values converge toward the tail of the symbol survivors—hence the“converged” region 310). The converged estimated symbol values will tendto be more accurate/reliable since they are based on more information.

There is also shown in FIG. 3 a symbol value histogram 402 (which may besimilar to one or more of the histograms shown in FIGS. 4A-4E) which maybe computed based on estimated symbol values within the observationregion 312 of the symbol survivors 300-303. Soft decisions 240 may begenerated based on a computed symbol value histogram 402.

The location of the observation region 312 may be determined (and acorresponding parameter set) based on a trade-off between the diversityprovided by the diverged region 320 and the reliability provided by theconverged region 310. That is, the location of the observation region312 may be selected such that the symbol values for the various symbolsurvivors 300-303 are sufficiently different to provide greater thanzero count for more than one symbol value, yet provide sufficientlyreliable symbol estimations. The observation region 312 may be aless-diverged sub-region within the diverged region 320 as compared toother (further to the left, in FIG. 3) sub-regions within the divergedregion 320.

The depth of the observation region 312 may be determined (and acorresponding parameter set) based on, for example, variability inlocation of the symbol survivors at which a determined percentage (e.g.,90%) of the symbol survivors converge to the same estimated value for aparticular symbol. If, for example, the depth of the observation region312 is set to one, but located at a position where the estimated valuesof a particular symbol have already converged, then the histogram 402will have zero counts for all but one possible symbol value. If, on theother hand, the depth of the observation region 312 is set to one, butthe location is at a position where the estimates of a particular symbolare widely divergent, then the histogram 402 may equal counts formultiple possible symbol values. By setting the depth of the observationregion 312 to greater than one, some averaging is achieved whereby, evenif the estimated values of a particular symbol corresponding to a groupof subwords were widely diverged at the front of the observation region312, and fully converged by the time they reached the tail of theobservation region 312 (x iterations of the sequence estimation processlater, for a depth of x symbols), the averaging effect may still resultin a histogram that provides useful information as to the probabilitiesof the various possible values for the transmitted constellationsymbols.

FIGS. 4A-4E illustrate generation of example histograms from symbolsurvivors in an RSSE circuit, in accordance with an embodiment of thedisclosure. While FIGS. 4A-4F use an 8-QAM symbol constellation andmaintenance of 8 survivors during the RSSE process (hence the totalcount in each of FIGS. 4A and 4B sums to 8) for purposes ofillustration, any symbol constellation may be used and any number ofsurvivors may be maintained. In this regard, the number of survivorsmaintained need not be equal to the number of points in theconstellation. For example, decoding circuit 116 may decode a signalgenerated with an M-QAM constellation by storing N survivors per symboltime, where N may be greater than, equal to, or less than M.

In each of FIGS. 4A and 4B, is shown an example constituent symbol valuehistogram for a particular transmitted symbol to be estimated. In eachof FIGS. 4C and 4D is shown a combined histogram generated from theconstituent histograms of FIGS. 4A and 4B.

The horizontal axis (x-axis) of the symbol value histograms in FIGS.4A-4D represent the set of 8-QAM symbol values from which estimatesymbol values are to be selected. The vertical axis (y-axis) of thesymbol value histograms in FIG. 4A-4D represent a count of the number oftimes, at a particular decision delay within the observation region 312of the survivors 300-303, that a particular received symbol wasestimated to have a particular value. In another example implementation,the vertical axis may be a weighted count calculated using apredetermined rule.

As an example of a predetermined rule, occurrences of one or more valuesmay be weighted by the aggregate metric of the survivor in which theoccurrence occurred. This metric may scale as the log probability of therespective path. For example, if the metric for survivor 300 is M300 andthe metric for survivor 301 is M301, then an occurrence in survivor 300may count as f(M300) and an occurrence in survivor 301 may count asf(M301), where f( ) is a predefined function.

As another example of a predetermined rule, the count of occurrences fora particular symbol value may be set to the maximum count occurring forthat symbol value in any one of the constituent histograms. For example,if two histograms are generated, “value1” is counted X times for symbol1in the first histogram, a value of “value1” is counted Y times forsymbol1 in the second histogram, and X>Y, then the count of “value1” forsymbol1 may be set to X, where the first histogram was generated duringone iteration of an RSSE process for a particular received symbol andthe second histogram was generated during another iteration of the RSSEprocess for the same particular received symbol.

As another example of a predetermined rule, the count of occurrences fora particular symbol value may be set to the average count occurring forthat symbol value over all of the constituent histograms. For example,if two histograms are generated, a value of “value1” is counted X timesfor symbol1 in the first histogram, and a value of “value1” is counted Ytimes for symbol1 in the second histogram, then the count of “value1”for symbol1 may be set to (X+Y)/2. These rules are merely examples forillustration. Other predefined rules are possible.

For simplicity of illustration, it is assumed the depth of theobservation window 312 is two. The histogram of FIG. 4A corresponds tosymbol time n, when the symbol of interest is in the first (left-most)position of the two-element observation window 312. The histogram ofFIG. 4B corresponds to symbol time n+1, when the symbol of interest isin the second (right-most) position of the two-element observationwindow 312. A combined histogram may be generated via linear ornonlinear combination of the constituent histograms. FIGS. 4C and 4Dillustrate two example combined histograms.

FIG. 4C shows a combined histogram generated using the constituenthistograms of FIGS. 4A and 4B with uniform weighting (e.g., bothhistograms weighted by a factor of 1). For the histogram shown in FIG.4C, the counts from FIG. 4A are simply added to the counts from FIG. 4B.Table 1 shows a few selected results for such an implementation.

TABLE 1 Count (symbolx) P(symbolx) 1 1/16 4 4/16 8 8/16 12 12/16  1515/16 

FIG. 4D shows a combined histogram generated using non-uniform weightingof the constituent histograms of FIGS. 4A and 4B. The weights mayincrease as the symbol being estimated moves toward the convergenceregion (i.e., increase as the reliability of the estimates increase).For illustration, in FIG. 4D the histogram of FIG. 4A is given a weightof 1 and the histogram of FIG. 4B is given a weight of 2. Table 2 showsa few selected results for such an implementation.

TABLE 2 Count (symbolx) P(symbolx) 1 1/24 6 4/24 12 8/24 18 12/24  2315/24 

Another example may help further illustrate implementations which usenon-uniform weighting: Assume that the observation window depth is setto two. Further assume that, during the iteration of the sequenceestimation process when the symbol to be estimated is in the firstelement of the observation region 312, the particular symbol isestimated to be “symbol3” in survivor 300, “symbol6” in survivor 301,“symbol6” in survivor 302, and “symbol3” in survivor 303. Further assumethat, during the symbol time when the particular symbol is in the second(and, in this example, the last) element of the observation region 312,the particular symbol is estimated to be “symbol3” in survivor 300,“symbol6” in survivor 301, “symbol3” in survivor 302, and “symbol3” insurvivor 303. Given these assumptions, in an example implementationusing uniform weighting, the count for subword6 is 3 and the count forsubword3 is 5. Conversely, in an example implementation using weightedcounting, the count for subword6 is (2×F)+(1×T) and the count forsubword3 is (2×F)+(3×T), where F is the weight applied for occurrencesat the front of the observation region 312 and T is the weight appliedfor occurrences at the tail of the observation region 312 (e.g., T>F).

In an example implementation, described with respect to FIGS. 4E and 4F,the symbol values may be mapped to subword values, and then LLRs may becalculated for the subwords.

In an example implementation, the LLRs may be processed by a predefinedSNR-dependent or SNR-independent function in order to better match theLLRs calculated based on the histograms of the RSSE system to LLRs whichwould have been obtained had full state information been available. Forexample, as each final symbol histogram is derived from multiple(dependent) histograms for different decision delays, some postcalculation compression function may be employed in order partiallyremove the correlation between the constituent histograms.

In an example implementation, the constituent and/or combined histogramsmay be modified based on information beyond the estimates within theobservation region. For example, subword occurrences outside of theobservation window in the best symbol survivor (the symbol survivorhaving the lowest metric) may be included in the counts. Along theselines, the size of the observation window may vary across the survivorswith the observation window for a particular survivor being determinedbased on that survivors calculated branch metric. Likewise, theobservation window need not necessarily comprise a range of consecutivedecision delays but some set of non-consecutive delays.

Also shown in FIGS. 4C and 4D is a subword mapping for the example 8-QAMsymbol constellation. This mapping may be used to generate thehistograms shown in FIGS. 4E and 4F.

Referring to FIG. 4E, the total count of “1”s for subword1 in FIG. 4C is8, the total count of “1”s for subword2 in FIG. 4C is 10 and the totalcount of “1”s for subword3 in FIG. 4C is 10. The corresponding LLRs areshown in table 3.

TABLE 3 Subword P(“1”) LLR 1  8/16 0 2 10/16 −0.22 3 10/16 −0.22

Referring to FIG. 4F, the total count of “1”s for subword1 in FIG. 4D is12, the total count of “1”s for subword2 in FIG. 4D is 16 and the totalcount of “1”s for subword3 in FIG. 4D is 15. The corresponding LLRs areshown in table 4.

TABLE 4 Subword P(“1”) LLR 1 12/24 0 2 16/24 −0.30 3 15/24 −0.22

In an example implementation, circuitry of a receiver (e.g., 130) may beoperable to receive an inter-symbol correlated (ISC) signal (e.g., 201),and generate a plurality of soft decisions (e.g., 240) as to informationcarried in the ISC signal. The soft decisions may be generated using areduced-state sequence estimation (RSSE) process. The RSSE process maybe such that the number of symbol survivors retained after eachiteration of the RSSE process is less than the maximum likelihood statespace. The soft decisions may be made available to a forward errorcorrection (FEC) decoder (e.g., via an inter-chip or intra-chip signalbus). The ISC signal may be received via a channel having a significantamount of nonlinearity. The nonlinearity may degrade performance metricin the circuitry by less than 1 dB, relative to a perfectly linearchannel, whereas, in a full response communication system, such anamount of nonlinearity would degrade the performance metric by 1 dB ormore, relative to a perfectly linear channel. The plurality of softdecisions may comprise a plurality of log likelihood ratios (LLRs). Eachof the plurality of LLRs may correspond to a respective one of aplurality of subwords of a forward error correction (FEC) codeword. TheRSSE process may comprise generation of a plurality of symbol survivorvectors, and analysis of contents of the plurality of symbol survivorvectors. The analysis may comprise determining a measure of probability,within an observation region of the plurality of symbol survivorvectors, for each one of a plurality of possible values of the ISCsignal (e.g., a probability for each of the 8-QAM values in FIGS.4A-4F). The measure of probability may be modified based on occurrencesof one or more of the possible values outside the observation region ina best symbol survivor (e.g., modify the measure of probability based onsymbol value occurrences outside the region 312 in the symbol survivor300, where 300 is the best symbol survivor). The measure of probabilityfor any particular possible value of the ISC signal may be a count ofoccurrences of the particular possible value within the observationregion (e.g., counting occurrences of estimated values within anobservation region 312 of the survivors 300-303). The possible values ofthe ISC signal may be symbol constellation values and/or FEC subwordvalues.

Other embodiments of the disclosure may provide a non-transitorycomputer readable medium and/or storage medium, and/or a non-transitorymachine readable medium and/or storage medium, having stored thereon, amachine code and/or a computer program having at least one code sectionexecutable by a machine and/or a computer, thereby causing the machineand/or computer to perform the steps as described herein for improvingBER performance based on a sequence estimation algorithm and FEC.

Accordingly, aspects of the present disclosure may be realized inhardware, software, or a combination of hardware and software. Aspectsof the present disclosure may be realized in a centralized fashion in atleast one computer system or in a distributed fashion where differentelements are spread across several interconnected computer systems. Anykind of computer system or other apparatus adapted for carrying out themethods described herein is suited. A typical combination of hardwareand software may be a general-purpose computer system with a computerprogram that, when being loaded and executed, controls the computersystem such that it carries out the methods described herein.

Aspects of the present disclosure may also be embedded in a computerprogram product, which comprises all the features enabling theimplementation of the methods described herein, and which when loaded ina computer system is able to carry out these methods. Computer programin the present context means any expression, in any language, code ornotation, of a set of instructions intended to cause a system having aninformation processing capability to perform a particular functioneither directly or after either or both of the following: a) conversionto another language, code or notation; b) reproduction in a differentmaterial form.

While the present disclosure has been described with reference tocertain embodiments, it will be understood by those skilled in the artthat various changes may be made and equivalents may be substitutedwithout departing from the scope of the present disclosure. In addition,many modifications may be made to adapt a particular situation ormaterial to the teachings of the present disclosure without departingfrom its scope. Therefore, it is intended that the present disclosurenot be limited to the particular embodiment disclosed, but that thepresent disclosure will include all embodiments falling within the scopeof the appended claims.

What is claimed is:
 1. A system comprising: signal processing circuitryand sequence estimation circuitry, wherein: said signal processingcircuitry is operable to receive a signal resulting from a transmittedplurality of symbols, each of said plurality of symbols corresponding toa plurality of subwords; said signal processing circuitry is operable tooutput samples of said received signal to said sequence estimationcircuitry; said sequence estimation circuitry is operable to processsaid samples to generate a plurality of vectors, where each of saidplurality of vectors represents a hypothesis as to the values of saidplurality of symbols; and said sequence estimation circuitry is operableto generate soft-decisions as to values of said plurality of symbolsand/or values of said plurality of subwords based on a count ofoccurrences of a particular symbol value and/or particular subword valuein said plurality of vectors.
 2. The system of claim 1, wherein a weightis applied to each one of said occurrences during generation of saidcount of occurrences.
 3. The system of claim 2, wherein said weightapplied to said one of said occurrences is based on one or both of:which one of said plurality of vectors said one of said occurrences isin; and a metric calculated for said one of said plurality of vectors.4. The system of claim 2, wherein: when said one of said plurality ofvectors is a first vector having a first metric, said weight applied tosaid one of said occurrences is a first weight based on said firstmetric; and when said one of said plurality of vectors is a secondvector having a second metric, said weight applied to said one of saidoccurrences is a second weight based on said second metric.
 5. Thesystem of claim 1, wherein said count of occurrences includes multipledecision delays in said plurality of vectors.
 6. The system of claim 5,wherein: a weight is applied to each one of said occurrences duringgeneration of said count of occurrences; and said weight is based onwhich one of said multiple decision delays said one of said occurrencesis at.
 7. The system of claim 6, wherein: when said one of saidoccurrences is at a first one of said multiple decision delays, saidweight is a first weight; and when said one of said occurrences is at asecond one of said multiple decision delays, said weight is a secondweight.
 8. The system of claim 1, wherein said sequence estimationcircuitry is operable to process said soft-decisions using asignal-to-noise ratio (SNR)-dependent function.
 9. The system of claim1, wherein one of said soft-decisions corresponding to one of saidplurality of symbols and/or one of said plurality of subwords is basedon a ratio of (i) said count of occurrences of said particular symbolvalue and/or particular subword value in said plurality of vectors to(ii) a count of occurrences of one or more other particular symbolvalues and/or particular subword values in said plurality of vectors.10. The system of claim 1, wherein each of said plurality of symbols isa quadrature amplitude modulation (QAM) symbol and each of saidplurality of subwords is a bit.
 11. A method comprising: performing in areceiver comprising signal processing circuitry and sequence estimationcircuitry: receiving, by said signal processing circuitry, an signalresulting from a transmitted plurality of symbols, each of saidplurality of symbols corresponding to a plurality of subwords;outputting, by said signal processing circuitry, samples of saidreceived signal to said sequence estimation circuitry; processing, bysaid sequence estimation circuitry, said samples to generate a pluralityof vectors, where each of said plurality of vectors represents ahypothesis as to the values of said plurality of symbols; andgenerating, by said sequence estimation circuitry, soft-decisions as tovalues of said plurality of symbols and/or values of said plurality ofsubwords based on a count of occurrences of a particular symbol valueand/or subword value in said plurality of vectors.
 12. The method ofclaim 11, comprising: applying, by said sequence estimation circuitry, aweight to each one of said occurrences as part of generating said countof occurrences.
 13. The method of claim 12, wherein said weight appliedto said one of said occurrences is based on one or both of: which one ofsaid plurality of vectors said one of said occurrences is in; and ametric calculated for said one of said plurality of vectors.
 14. Themethod of claim 12, wherein: when said one of said plurality of vectorsis a first vector having a first metric, said weight applied to said oneof said occurrences is a first weight based on said first metric; andwhen said one of said plurality of vectors is a second vector having asecond metric, said weight applied to said one of said occurrences is asecond weight based on said second metric.
 15. The method of claim 11,wherein said count of occurrences includes multiple decision delays insaid plurality of vectors.
 16. The method of claim 15, comprising:applying, by said sequence estimation circuitry, a weight to each one ofsaid occurrences as part of generating of said count of occurrences,wherein said weight is based on which one of said multiple decisiondelays said one of said occurrences is at.
 17. The method of claim 16,wherein: when said one of said occurrences is at a first one of saidmultiple decision delays, said weight is a first weight; and when saidone of said occurrences is at a second one of said multiple decisiondelays, said weight is a second weight.
 18. The method of claim 11,comprising processing, by said sequence estimation circuitry, saidsoft-decisions using a signal-to-noise ratio (SNR)-dependent function.19. The method of claim 11, wherein one of said soft-decisionscorresponding to one of said plurality of symbols and/or one of saidplurality of subwords is based on a ratio of (i) said count ofoccurrences of said particular symbol value and/or subword value in saidmultiple survivor vectors to (ii) a count of occurrences of one or moreother particular symbol values and/or particular subword values in saidplurality of vectors.
 20. The method of claim 11, wherein each of saidplurality of symbols is a quadrature amplitude modulation (QAM) symboland each of said plurality of subwords is a bit.